diff --git a/jsonschema/_validators.py b/jsonschema/_validators.py
index 9a07f5ec3..874e8796f 100644
--- a/jsonschema/_validators.py
+++ b/jsonschema/_validators.py
@@ -418,6 +418,8 @@ def if_(validator, if_schema, instance, schema):
 
 
 def unevaluatedItems(validator, unevaluatedItems, instance, schema):
+    if not validator.is_type(instance, "array"):
+        return
     evaluated_item_indexes = find_evaluated_item_indexes_by_schema(
         validator, instance, schema,
     )
@@ -431,6 +433,8 @@ def unevaluatedItems(validator, unevaluatedItems, instance, schema):
 
 
 def unevaluatedProperties(validator, unevaluatedProperties, instance, schema):
+    if not validator.is_type(instance, "object"):
+        return
     evaluated_property_keys = find_evaluated_property_keys_by_schema(
         validator, instance, schema,
     )
diff --git a/jsonschema/tests/test_jsonschema_test_suite.py b/jsonschema/tests/test_jsonschema_test_suite.py
index 60f52a97a..2d807b77b 100644
--- a/jsonschema/tests/test_jsonschema_test_suite.py
+++ b/jsonschema/tests/test_jsonschema_test_suite.py
@@ -346,11 +346,6 @@ def leap_second(test):
             message="unevaluatedItems is different in 2019-09 (needs work).",
             subject="unevaluatedItems",
         )(test)
-        or skip(
-            message=bug(949),
-            subject="unevaluatedProperties",
-            case_description="non-object instances are valid",
-        )(test)
         or skip(
             message="dynamicRef support isn't working yet.",
             subject="recursiveRef",
@@ -416,16 +411,6 @@ def leap_second(test):
             message="Vocabulary support is not yet present.",
             subject="vocabulary",
         )(test)
-        or skip(
-            message=bug(949),
-            subject="unevaluatedItems",
-            case_description="non-array instances are valid",
-        )(test)
-        or skip(
-            message=bug(949),
-            subject="unevaluatedProperties",
-            case_description="non-object instances are valid",
-        )(test)
         or skip(
             message=bug(),
             subject="ref",
diff --git a/jsonschema/tests/test_validators.py b/jsonschema/tests/test_validators.py
index 23655a163..3aabd3370 100644
--- a/jsonschema/tests/test_validators.py
+++ b/jsonschema/tests/test_validators.py
@@ -597,6 +597,11 @@ def test_unevaluated_items(self):
             "Unevaluated items are not allowed ('bar', 'foo' were unexpected)",
         )
 
+    def test_unevaluated_items_on_invalid_type(self):
+        schema = {"type": "array", "unevaluatedItems": False}
+        message = self.message_for(instance="foo", schema=schema)
+        self.assertEqual(message, "'foo' is not of type 'array'")
+
     def test_unevaluated_properties(self):
         schema = {"type": "object", "unevaluatedProperties": False}
         message = self.message_for(
@@ -612,6 +617,11 @@ def test_unevaluated_properties(self):
             "('bar', 'foo' were unexpected)",
         )
 
+    def test_unevaluated_properties_on_invalid_type(self):
+        schema = {"type": "object", "unevaluatedProperties": False}
+        message = self.message_for(instance="foo", schema=schema)
+        self.assertEqual(message, "'foo' is not of type 'object'")
+
 
 class TestValidationErrorDetails(TestCase):
     # TODO: These really need unit tests for each individual validator, rather